The Predators have been touting the fact that Shea Weber is having probably the best season of his career.

So it’s no major surprise that they have started a Norris Trophy campaign of sorts for the veteran defenseman.

Weber is on pace for a career high in goals (he currently has 20) and points (he currently has 50) and averages 26:52 ice time per game (highest of his career). The campaign includes a video.

“I think he’s having his best season, I think he’s a dominant force on the blueline,” coach Barry Trotz said. “I think he has been exceptional. He’s leading all defensemen in categories, and being in a small market he doesn’t get the love you get in a more traditional large market.”

Weber is a two-time finalist for the Norris Trophy — given to the best all-around defenseman in the NHL — but has been a runner-up twice. Helost to sentimental favorite Nicklas Lidstrom in 2010-11 despite the fact Weber had better all-around numbers, and in 2011-12 he lost to offensive dynamo Erik Karlsson, who hardly played on the penalty kill.

This season, Weber’s plus/minus may be his undoing. Though he’s a minus-6, Nashville’s offense has been slow, and its defense has been without star goaltender Pekka Rinne for most of the season. It’s tough to blame Weber for the minus-6.

Weber was not exactly in the chattiest of moods about the Norris Trophy on Friday after the morning skate for tonight’s game against the Ducks (9 p.m., SportSouth, 102.5-FM).

“I’m not thinking about that type of stuff,” Weber said. “I don’t like self promotion and I don’t like that kind of stuff. I’m focused on the team in here and winning games and finishing out the season strong.”